To improve the driving performance of vehicles, it is of great significance to study the changes in the driver's brain cognition during driving and to establish an intelligent driving computational framework based on the cognitive process. Electroencephalogram (EEG) is an effective means to study driver cognition because of its low cost, high temporal resolution, and different cognitive state information. The application of brain-computer interface (BCI) technology based on EEG signals to driver assistance systems has the potential to transform the way humans interact with vehicles. It can also help intelligent vehicles to understand and predict driver's behavior and to enhance the cognitive ability of vehicles. This article reviews the research on theorizing and modeling driver cognitive processes based on cognitive architectures (e.g., adaptive control for thoughtful rationality (ACT-R), queuing network (QN), and Soar) and proposes an EEG-based driver cognitive architecture. Then, according to the relationship between the modules of this proposed driver cognitive architecture, the driver's perception of stationary and hazardous scenarios in the driving environment, the understanding of the driver's intention to control the longitudinal and lateral movements of the vehicle, and the influence of driver's working memory as well as human factors, such as fatigue, distraction, and emotion on driving performance based on EEG signals, are reviewed. The integration of EEG signals with cognitive modeling has the potential to improve the accuracy of driver perception, intention, and cognitive state prediction, thereby enhancing vehicle safety.